The sum of all $x \in[0, \pi]$ which satisfy the equation $\sin x+\frac{1}{2} \cos x=\sin ^2\left(x+\frac{\pi}{4}\right)$ is
$\frac{\pi}{6}$
$\frac{5 \pi}{6}$
$\pi$
$2 \pi$
If $e ^{\left(\cos ^{2} x+\cos ^{4} x+\cos ^{6} x+\ldots \ldots \infty\right) \log _{e} 2}$ satisfies the equation $t ^{2}-9 t +8=0,$ then the value of $\frac{2 \sin x}{\sin x+\sqrt{3} \cos x}\left(0 < x < \frac{\pi}{2}\right)$ is
If $\frac{{1 - {{\tan }^2}\theta }}{{{{\sec }^2}\theta }} = \frac{1}{2}$, then the general value of $\theta $ is
One root of the equation $\cos x - x + \frac{1}{2} = 0$ lies in the interval
The number of solution of the equation $2\cos ({e^x}) = {5^x} + {5^{ - x}}$, are
The general solution of the trigonometric equation $\tan \theta = \cot \alpha $ is